The first overtone of a stretched string of given length is 320 Hz. The first harmonic is

Options

A. `320Hz`
B. `640Hz`
C. `160Hz`
D. `480Hz`

Explanation

To find the first harmonic (fundamental frequency) of a stretched string given that the first overtone is 320 Hz, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between harmonics and overtones**:
- The first harmonic (fundamental frequency) is denoted as \( f \).
- The first overtone corresponds to the second harmonic, which is \( 2f \).

2. **Use the information given**:
- We know that the first overtone is 320 Hz. Since the first overtone is the second harmonic, we can write:
\[ 2f = 320 \text{ Hz} \]

3. **Solve for the fundamental frequency**:
- To find the fundamental frequency \( f \), we can rearrange the equation:
\[ f = \frac{320}{2} \]
- Calculating this gives:
\[ f = 160 \text{ Hz} \]

4. **Conclusion**:
- Therefore, the first harmonic (fundamental frequency) of the stretched string is 160 Hz.

### Final Answer:
The first harmonic is **160 Hz**.

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